In how many ways can the letters of word ACCOUNTANT be arranged if vowels always occur together.

The word ACCOUNTANT has 10 letters, including 4 vowels (A, O, U, A) and 6 consonants (C, C, N, T, N, T). When the vowels always occur together, treat them as a single unit. This vowel unit, along with the 6 consonants, creates 7 units to arrange. These 7 units can be arranged in 7! divided by (2! for C, 2! for N, and 2! for T) ways. The 4 vowels within their unit can be arranged in 4! divided by 2! ways. Multiplying these gives the result: (7! divided by 8) times (4! divided by 2), which equals 630 times 12, or 7560.

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